# Large Salem Sets Avoiding Nonlinear Configurations

@inproceedings{Denson2021LargeSS, title={Large Salem Sets Avoiding Nonlinear Configurations}, author={Jacob Denson}, year={2021} }

We construct large Salem sets avoiding patterns, complementing previous constructions of pattern avoiding sets with large Hausdorff dimension. For a (possibly uncountable) family of uniformly Lipschitz functions tfi : pT qn ́2 Ñ Tu, we obtain a Salem subset of T with dimension d{pn ́ 1q avoiding nontrivial solutions to the equation xn ́ xn ́1 “ fipx1, . . . , xn ́2q. For a countable family of smooth functions tfi : pT qn ́1 Ñ Tu satisfying a modest geometric condition, we obtain a Salem…

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